Yet Another Entropy Power Inequality With an Application

In this paper, the authors derive a generalization of the vector Entropy Power Inequality (EPI) recently put forth in, which was valid only for diagonal matrices, to the full matrix case. Next, they study the problem of computing the linear precoder that maximizes the mutual information in linear vector Gaussian channels with arbitrary inputs. In particular, they transform the precoder optimization problem into a new form and, capitalizing on the newly unveiled matrix EPI, they show that some particular instances of the optimization problem can be cast in convex form, i.e., they can have an optimality certificate, which, to the best of their knowledge, had never been obtained previously.